Solve 23/4+11/8div21/2

$$2 \frac { 3 } { 4 } + 1 \frac { 1 } { 8 } \div 2 \frac { 1 } { 2 }$$

Evaluate

$$\frac{16}{5}=3.2$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\frac{8+3}{4}+\frac{\frac{1\times 8+1}{8}}{\frac{2\times 2+1}{2}}$$

Add 8 and 3 to get 11.

$$\frac{11}{4}+\frac{\frac{1\times 8+1}{8}}{\frac{2\times 2+1}{2}}$$

Divide \frac{1\times 8+1}{8} by \frac{2\times 2+1}{2} by multiplying \frac{1\times 8+1}{8} by the reciprocal of \frac{2\times 2+1}{2}.

$$\frac{11}{4}+\frac{\left(1\times 8+1\right)\times 2}{8\left(2\times 2+1\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{11}{4}+\frac{1+8}{4\left(1+2\times 2\right)}$$

Add 1 and 8 to get 9.

$$\frac{11}{4}+\frac{9}{4\left(1+2\times 2\right)}$$

Multiply 2 and 2 to get 4.

$$\frac{11}{4}+\frac{9}{4\left(1+4\right)}$$

Add 1 and 4 to get 5.

$$\frac{11}{4}+\frac{9}{4\times 5}$$

Multiply 4 and 5 to get 20.

$$\frac{11}{4}+\frac{9}{20}$$

Least common multiple of 4 and 20 is 20. Convert \frac{11}{4} and \frac{9}{20} to fractions with denominator 20.

$$\frac{55}{20}+\frac{9}{20}$$

Since \frac{55}{20} and \frac{9}{20} have the same denominator, add them by adding their numerators.

$$\frac{55+9}{20}$$

Add 55 and 9 to get 64.

$$\frac{64}{20}$$

Reduce the fraction \frac{64}{20} to lowest terms by extracting and canceling out 4.

$$\frac{16}{5}$$

Factor

$$\frac{2 ^ {4}}{5} = 3\frac{1}{5} = 3.2$$